Evolutionary plasticity and innovations in complex metabolic reaction networks

Abstract

Genome-scale metabolic networks are highly robust to the elimination of enzyme-coding genes. Their structure can evolve rapidly through mutations that eliminate such genes and through horizontal gene transfer that adds new enzyme-coding genes. Using flux balance analysis we study a vast space of metabolic network genotypes and their relationship to metabolic phenotypes, the ability to sustain life in an environment defined by an available spectrum of carbon sources. Two such networks typically differ in most of their reactions and have few essential reactions in common. Our observations suggest that the robustness of the Escherichia coli metabolic network to mutations is typical of networks with the same phenotype. We also demonstrate that networks with the same phenotype form large sets that can be traversed through single mutations, and that single mutations of different genotypes with the same phenotype can yield very different novel phenotypes. This means that the evolutionary plasticity and robustness of metabolic networks facilitates the evolution of new metabolic abilities. Our approach has broad implications for the evolution of metabolic networks, for our understanding of mutational robustness, for the design of antimetabolic drugs, and for metabolic engineering.

Figure 1. Exploration of a vast genotype space of metabolic networks.

A genotype can be represented in different ways: (A) as a metabolic network, (B) as a node in a genotype network, or (C) as a binary vector listing the reactions catalyzed. Genotypes on the genotype network (B) that are connected differ by only one mutation. The color of the genotype circles indicates their metabolic phenotype. Metabolic phenotypes are computed using FBA applied to 101 environments with different carbon sources. They can be represented as a binary vector listing the environments a genotype is viable in (D). Random evolutionary walks can be seen as paths on a genotype network. Two independent random walks are shown with the same starting genotype (G1) and two final genotypes (GF and GF'), passing through intermediate genotypes (i.e.: G2) that differ by one mutation. Mutations are chosen at random. They can be additions or deletions of individual reactions from the corresponding metabolic network but they must not change the phenotype. The neighborhood of each genotype can be analyzed by characterizing the phenotype of the one mutant neighbor genotypes (approximately 5’800 neighbors per genotype). The number of genotypes in the genotype space is 2⁵⁸⁰⁰. Each genotype is able to catalyze approximately 1000 out of 5800 possible reactions.

Figure 2. Essential reactions differ dramatically between metabolic networks with the same metabolic abilities.

(A) Distribution of the fraction of essential reactions in 1000 random networks viable in minimal or rich glucose containing medium. (B) Distribution of the fraction of essential reactions shared among pairs of these 1000 random networks. (C) Rank plot of reaction essentiality. Reactions essential in all of the 1000 random viable networks are given the lowest rank of one. (D) The average fraction of essential reactions (vertical axis) as a function of the number of carbon sources a network can sustain life in (horizontal axis). Each point is an average of 100 networks (whiskers: 95% confidence interval).

Figure 3. Reaction essentiality in central metabolism.

Color-coded map of reactions in central energy metabolism that appear rarely (blue) or frequently (red) as essential in 1000 random viable metabolic networks. The color is in logarithmic scale indicating that most reactions even in this most central part of metabolism are essential only in a small fraction of networks with a given metabolic phenotype.

Figure 4. Metabolic networks with the same phenotype can have vastly different genotypes.

(A) Distribution of maximum genotype distance between 1000 networks that are the end-points of random walks leading away from the initial (E. coli) network while preserving the metabolic phenotype. (B) Maximum genotype distances (vertical axis) between initial metabolic networks able to sustain life on a given number of carbon sources (horizontal axis) and 1000 final random viable metabolic networks. For each number of carbon sources 100 random walks of 10⁴ mutations were carried out starting from 10 different initial networks (whiskers: 95% confidence interval). (C) The distribution of minimal genotype distance between pairs of networks with different metabolic phenotypes required to sustain life on at least one carbon source. (D) Average minimal genotype distance (the mean of the distribution in (C) as a function of the number of carbon sources. The error bars are too short to be visible in this plot.

Figure 5. Evolving networks with conserved phenotypes can access very different novel phenotypes along their evolutionary path.

(A) shows the average cumulative number of phenotypes (vertical axis) found in the neighborhood of an evolving network as a function of the number of mutations (horizontal axis) the network experienced during its evolution; (B) shows the fraction of the phenotypes in the neighborhood of the evolving network (G_t) and an initial network (G₀) that differ from one another. The diagram in the inset illustrates the increasing number of novel phenotypes in the evolving network's neighborhood (gray area of the circle) that are different from the phenotypes in the neighborhood of G₀. For pairs of random viable metabolic networks with the same phenotype; (C) shows the distribution of the fraction of different phenotypes in the neighborhoods of these networks. (D) shows the mean of the distribution (C) of phenotypic differences in the neighborhood of the network pairs versus the numbers of carbon sources they can sustain growth on. Data in (A), (B), (C) and (D) are averages over 100 random walks of 10⁴ mutations starting from 10 different initial networks. In (C) only pairs of networks with the same initial network of the random walk were compared, thus 450 neighborhood comparisons. In all plots whiskers represent the 95% confidence interval.